If you were to change from LEO to full polar orbit around the Sun, and made no changes in distance, how much dV and how much Hydrox fuel would you consume? (Assume, say, a 1 metric ton satellite)
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If you were to change from LEO to full polar orbit around the Sun, and made no changes in distance, how much dV and how much Hydrox fuel would you consume? (Assume, say, a 1 metric ton satellite)
STARGAZING: All I see are the lights of a billion places I'll never go. --Howard Tayler, Schlock Mercenary
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Since the orbital speed and hight are the same there is not change in energy to consider.
To change orbits we would need to apply a torque to the orbit using a force perpendicular to the motion. Examining the intersection points of the orbits shows a dV of sqrt(2)V. So, if we have an object with an orbital speed of 7 km/s, we would have a dV of roughly 10 km/s.
In general, to rotate the inclination of an orbit with momentum P by an angle θ requires a change in momentum of 2P*sin(θ/2).
It would be less expensive on fuel to pay the initial 500 m/s bonus from the rotation of the Earth at launch, and use a high latitude launching site.
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The velocity change would be expensive enough that in the case of Ulysses, they sent the spacecraft out to Jupiter for a swing-by/gravity assist maneuver:
http://www.rssd.esa.int/helio/missio...ter_flyby.html
http://www.rssd.esa.int/helio/missio..._appendix.html
I say there is an invisible elf in my backyard. How do you prove that I am wrong?
The Leif Ericson Cruiser
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Wait! You say Polar orbit about the SUN. My previous comment was for a polar orbit about the Earth.Originally Posted by Noclevername
The circular orbital velocity is half the escape velocity. For an orbit with a velocity of 7 km/s relative to Earth we would need another 7 km/s to escape Earth. Our satellite would then be in a nearly circular orbit about the sun with a speed of 30 km/s and an inclination of 7 degrees.
Using the dV=2Vsin(θ/2) equation from my previous post we would need an additional dV of 40 km/s to get to a polar orbit.
This gives a total dV of 47 km/s.
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Next time I'll write it in large print. ; )
STARGAZING: All I see are the lights of a billion places I'll never go. --Howard Tayler, Schlock Mercenary
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It's essentially impossible with a hydrolox rocket (LH2/LOX chemical rocket). As Van Rijn notes, it's better to do a Jupiter flyby. Even so, this won't put you into a circular polar orbit with a 1AU radius. You can get a 1AU perihelion pretty easily, but you won't have enough delta-v to transition from that eliptical orbit to a circular 1AU orbit.
Roughly, you need a v_inf a bit more than 15km/s to get to the desired Earth->Jupiter transfer orbit. From LEO, this requires about sqrt(15^2+11^2) -7.8 = 11km/s. This is pretty steep, but doable with a mass ratio of around 12. Not counting fuel required for stationkeeping and fine midcourse corrections, the flyby around Jupiter is for free. This will put you in a polar orbit with an aphelion around 5AU. You can choose the perihelion at 1AU if you want.
But making a transition from this elliptical orbit to a circular 1AU orbit would require about 15km/s more delta-v, which gets into ridiculously undoable mass ratios.
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From LEO, a best case scenario for a direct orbital injection (assuming that the LEO already was at the exact inclination and orientation such that the hyperbolic excess velocity vector away from earth was correct) would be around 36 km/s. That's pretty much impossible. With a fairly creative use of multiple gravity assists as well as carefully timed engine burns, it might be possible to get this down to a reasonable value, but I don't know what exactly that could bring it down to.
Also, note that with this scheme, hydrolox would be effectively undoable. This would require propellants which could be fired possibly years after launch, and hydrolox really isn't storable for that length of time due to boiloff. So, the available delta-V is a bit lower, due to the need for storable propellants.
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Or electrolyze water as you go.
Whatcha using this orbit for, a solar observatory for flares/CMEs? I wonder if a solar sail would work better, perhaps using a dive maneuver.
Et tu BAUT? Quantum mutatus ab illo.
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I'm thinking of using it for a story, with a Mysterious MacGuffin found floating over the Sun's north pole at about 1 AU. How does it stay there? That's the Mystery!
STARGAZING: All I see are the lights of a billion places I'll never go. --Howard Tayler, Schlock Mercenary
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I think that given the relatively unmoving nature of the MM, I'm probably going with a solar sail. That rather complicates the calculations, however, and I barely understood the orbital machanics of the rocket idea. How big a sail do you think I would need, and how long would it take to reach the objective?
STARGAZING: All I see are the lights of a billion places I'll never go. --Howard Tayler, Schlock Mercenary
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It seems like a solar sail, such that the radiation and gravitational pressure are equal, could explain how it stays there. If it were a space faring vessel adjustable enough to steer there, it should be more than adjustable enough to make the corrections needed to maintain its distance and position.
The vessel can maintain a weight of 1543 kg per square kilometer of sail. If the vessel is angled at 45 degrees its rest area, it would be able to produce a thrust of 40% of its mass, but would only support 1,100 kg per square km of sail.
Let us not forget the weight of the sail. State of the art carbon fiber sails have an area density of 3 g/m^2, or 3,000 kg/km^2. Thus our sail would need to be 3 times less dense than carbon fiber to break even.
Nano-tub mesh weaves can attain 100 kg/km^2, but producing this material on this scale is problematic. This would give a payload of 1,000 kg per square km of sail in the previously mentioned rest mode.
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Are you talking about a statite? That's different from a spacecraft in a polar orbit. A polar orbit is just a matter of inclination, but a statite would require constant thrust to maintain its position.
I say there is an invisible elf in my backyard. How do you prove that I am wrong?
The Leif Ericson Cruiser
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I was thinking of using a solar sail to reach the Mystery Object from Earth. The Object is not a statite, that would be an easy mystery to solve. Once the sail reaches its objective, it might become a statite and "hover" near the Object.
STARGAZING: All I see are the lights of a billion places I'll never go. --Howard Tayler, Schlock Mercenary
Order of Kilopi
You could use a magnetic sail to thrust at right angles to the solar wind. If you want to get advanced, it use plasma. It won't be able to hover, but maybe it will be able to orbit that point above the sun's pole. I wonder if a sun dive would help with a magnetic sail.
Et tu BAUT? Quantum mutatus ab illo.
Order of Kilopi
For a flyby or impact mission, a Jupiter flyby is the best option. This takes about 11km/s from LEO for a direct transfer to Jupiter, but potentially much less if you're willing to use multiple Venus/Earth flybies like Galileo.
A solar sail with statite capability could nullify thrust sideways toward the Sun, producing a net force toward a point halfway between Earth and the mystery object. It could then do a 180 degree arc of a circular orbit around this point. The orbital radius is .707AU and the inward force is 1.414 times; these effects cancel each other out on the orbital speed. So, the sail travels around this arc at 30km/s, taking about 4 months to reach the mystery object. Before reaching the mystery object, it will have to slow down to nullify its orbital speed. This is a more complex calculation, but it should take somewhere less than 3 months (a quarter orbit). The two phases really combine, so it could take a total of somewhere around 5 or 6 months.
Note that a solar sail with statite capability is extremely advanced. It's far beyond anything we can do with today's technology.
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